Time-Interleaved ADCs - Theory and Design - El-Chammas

1 Time-Interleaved ADCsTheory and DesignManar El-ChammasTexas InstrumentsDecember 11, 2011 Who am I?Received from in 2004 Received from Stanford University in 2010 IThesis: Background calibration of timing-skew in time -interleavedADCs Advisor: Boris MurmannIResearch interests: Integrated circuits, background calibration, lowpower designCurrently working at Texas Instruments (Dallas, TX) on high-speeddata convertersM. El-Chammas (TI) Time-Interleaved ADCsDec. 20112 / 158 Tutorial objectivesTo understand the Theory and operation of Time-Interleaved ADCsand how to Design themAt the end of this tutorial, youwillhave a toolbox to analyzetime- interleaved adcs withand astarting pointfrom which todesign one Stop me whenever you have questionsM. El-Chammas (TI) Time-Interleaved ADCsDec. 20113 / 158A broad-stroke outlineOverview of data convertersThe Time-Interleaved ADCQ uantitative analysis of time -varying errorsDesign of Time-Interleaved ADCsCalibrationM.

2 El-Chammas (TI) Time-Interleaved ADCsDec. 20114 / 158 Part IOverview of Data ConvertersM. El-Chammas (TI) Time-Interleaved ADCsDec. 20115 / 158 IntroductionData converters important part of signal chain[Slide taken from B. Murmann notes]M. El-Chammas (TI) Time-Interleaved ADCsDec. 20116 / 158 Data converter applicationsConsumer electronicsIVideo and audioIDigital camerasIAutomotive systemsCommunication systemsIWireless infrastructureIEthernetComputing and controlIStorage mediaIFeedback systemsInstrumentationIMedical equipmentIOscilloscopesM. El-Chammas (TI) Time-Interleaved ADCsDec. 20117 / 158 ExamplesAgilent oscilloscopePublished in ISSCC 2003M. El-Chammas (TI) Time-Interleaved ADCsDec. 20118 / 158 Examples1 kS/s ADC for medical implantsPublished in ESSCIRC 2010M. El-Chammas (TI) Time-Interleaved ADCsDec. 20119 / 158 ExamplesTI ADC used in wireless infrastructurePublished in ISSCC 2010M. El-Chammas (TI) Time-Interleaved ADCsDec.

3 201110 / 158 Reference booksPrinciples of Data Conversion System Design , Behzad RazaviData Converters, F. MalobertiCMOS Data Converters for Communications, Mikael Gustavsson et Delta-Sigma Data Converters, Richard Schreier et Conversion Handbook, Analog Devices El-Chammas (TI) Time-Interleaved ADCsDec. 201111 / 158 Analog-to-digital conversionDefinitionThe conversion from acontinuous-timesignal to adiscrete-timerepresentationADCINOUTM. El-Chammas (TI) Time-Interleaved ADCsDec. 201112 / 158 Analog-to-digital conversionAnalog-to-digital conversion consists of two operations ..SamplingQuantizationM. El-Chammas (TI) Time-Interleaved ADCsDec. 201113 / 158 Sampling and quantizationSampling(Discretizing in time )Quantization(Discretizing in amplitude)[Murmann notes]M. El-Chammas (TI) Time-Interleaved ADCsDec. 201114 / 158 Sampling and quantizationMost common approach is to discretizeuniformlyin both time andamplitudeThese two concepts alone can fill an entire semester.

4 For more on these, see reference booksM. El-Chammas (TI) Time-Interleaved ADCsDec. 201115 / 158 Types of adcs : the flash ADCF lash ADC has 2B 1 comparatorsExtremely fast with limited resolutionM. El-Chammas (TI) Time-Interleaved ADCsDec. 201116 / 158 Types of adcs : the pipeline ADCP ipeline adcs have moderate speed and high resolution[Image from B. Murmann notes]M. El-Chammas (TI) Time-Interleaved ADCsDec. 201117 / 158 Types of references previously mentioned discuss most of theseM. El-Chammas (TI) Time-Interleaved ADCsDec. 201118 / 158 Part IIThe Time-Interleaved ADCM. El-Chammas (TI) Time-Interleaved ADCsDec. 201119 / 158 Introduction to Time-Interleaved ADCsDefinitionAn ADC that cycles through a set ofNsub- adcs , such that the aggregatesample-rate isNtimes the sample-rate of the individual sub-ADCsM. El-Chammas (TI) Time-Interleaved ADCsDec. 201120 / 158 Introduction to Time-Interleaved ADCs0(t)x(t)y[n]ADC0 ADC1 ADCN-11(t)N-1(t).

5 Sub- adcs tend to be identicalM. El-Chammas (TI) Time-Interleaved ADCsDec. 201121 / 158 Back in 1980 ..William Black, thesis High Speed CMOS A/Dconversion techniques Published time -InterleavedConverter Arrays [Black 1980] This high speed technique was for a7-bit MHzADCM. El-Chammas (TI) Time-Interleaved ADCsDec. 201122 / 30 years laterTime- interleaved adcs are still a serious research areaMulti-GHZ adcs are thenormIAgilent, 2003: 80-way interleaved 20 GS/sIFujitsu, 2009: 4-way interleaved 56 GS/sINortel, 2010: 16-way interleaved 40 GS/sM. El-Chammas (TI) Time-Interleaved ADCsDec. 201123 / 158 How exactly does it work?Intuitive in the time -domainM. El-Chammas (TI) Time-Interleaved ADCsDec. 201124 / 158 First ADC samples the signal ..Example of Two interleaved Sub-ADCs12x(t)y[n]ADC0 ADC1x(t)M. El-Chammas (TI) Time-Interleaved ADCsDec. 201125 / 158 Second ADC samples the signal ..Example of Two interleaved Sub-ADCs13x(t)y[n]ADC0 ADC1x(t)M.

6 El-Chammas (TI) Time-Interleaved ADCsDec. 201126 / 158 And again, first ADC samples the signal ..Example of Two interleaved Sub-ADCs14x(t)y[n]ADC0 ADC1x(t)M. El-Chammas (TI) Time-Interleaved ADCsDec. 201127 / 158 time -domain analysisEach sub-ADC output is (ignoring quantization)yi[n] =x((nN+i)Ts)(1)whereTsis sampling period,Nis interleaving factor, andi= 0,..,N 1M. El-Chammas (TI) Time-Interleaved ADCsDec. 201128 / 158 time -domain analysis0(t)x(t)y[n]ADC0 ADC1 ADCN-11(t)N-1(t)..Output multiplexer combines these streams such thaty[n] =yi[n iN]wherei=nmodN(2)M. El-Chammas (TI) Time-Interleaved ADCsDec. 201129 / 158 Frequency-domain analysisThis is less intuitive ..Can take the discrete- time Fourier transform (DTFT) of the(upsampled) sub-ADC outputs and the Time-Interleaved ADC outputIn Theory , ..Y(f) =N 1 i=0Yi(f)(3)M. El-Chammas (TI) Time-Interleaved ADCsDec. 201130 / 158 Frequency-domain analysisAssume you have an input signal with the following |X(f)|fM.

7 El-Chammas (TI) Time-Interleaved ADCsDec. 201131 / 158 Frequency-domain analysisThe resulting (upsampled) sub-ADC output DTFT will |Y0(f)|fM. El-Chammas (TI) Time-Interleaved ADCsDec. 201132 / 158 Frequency-domain analysisReplicas have different phases for each of the sub-ADCsWhen summed, the phases cancel each other outYouwillget the same spectrum as the |Y(f)|fM. El-Chammas (TI) Time-Interleaved ADCsDec. 201133 / 158 time -varying errorsIn Theory , Theory and practice are the practice, they are El-Chammas (TI) Time-Interleaved ADCsDec. 201134 / 158 time -varying errorsIdeally, a Time-Interleaved ADC can be blackboxed into a singlemonolithic ADCM. El-Chammas (TI) Time-Interleaved ADCsDec. 201135 / 158 time -varying errorsOffsetGainTiming skew(Bandwidth)0(t-0)x(t)y[n]ADC0 ADC1 ADCN-11(t-1)N-1(t-N-1)oN-1GN-1o1G1o0G0.. M. El-Chammas (TI) Time-Interleaved ADCsDec. 201136 / 158 time -varying (t) (t) (t)Timing (t)M. El-Chammas (TI) Time-Interleaved ADCsDec.

8 201137 / 158 Sources of errorsPVT (Process, voltage, temperature) variationsCurrent flow, layout nonidealities, mismatch in stray capacitance, etc. All of these will limit your ADC performanceM. El-Chammas (TI) Time-Interleaved ADCsDec. 201138 / 158 Offset mismatchEach sub-ADCideallydigitizesx(t)yi[n] =x((nN+i)Ts)(4)Each sub-ADCactuallydigitizesx(t) +oiyi[n] =x((nN+i)Ts) +oi(5)oiis different for each sub-ADCM. El-Chammas (TI) Time-Interleaved ADCsDec. 201139 / 158 Frequency-domain |Y0(f)|fThe DTFT of the sub-ADC changes because of these offsetsM. El-Chammas (TI) Time-Interleaved ADCsDec. 201140 / 158 Frequency-domain |Y(f)|fThe DTFT of the ADC has spurs at frequenciesi fs/NM. El-Chammas (TI) Time-Interleaved ADCsDec. 201141 / 158 Gain mismatchEach sub-ADCideallydigitizesx(t)yi[n] =x((nN+i)Ts)(6)Each sub-ADCactuallydigitizesGix(t)yi[n] =Gix((nN+i)Ts)(7)Giis different for each sub-ADCM. El-Chammas (TI) Time-Interleaved ADCsDec. 201142 / 158 Frequency-domain |Y0(f)|fThe DTFT of the sub-ADC changes because of these gain differencesM.

9 El-Chammas (TI) Time-Interleaved ADCsDec. 201143 / 158 Frequency-domain |Y(f)|fThe DTFT of the ADC has replicas at frequenciesfin i fs/NM. El-Chammas (TI) Time-Interleaved ADCsDec. 201144 / 158 Timing skewEach sub-ADCideallydigitizesx(t)yi[n] =x((nN+i)Ts)(8)Each sub-ADCactuallydigitizesx(t i)yi[n] =x((nN+i)Ts i)(9) iis different for each sub-ADCM. El-Chammas (TI) Time-Interleaved ADCsDec. 201145 / 158 Frequency-domain |Y0(f)|fThe DTFT of the sub-ADC changes because of timing skewM. El-Chammas (TI) Time-Interleaved ADCsDec. 201146 / 158 Frequency-domain |Y(f)|fThe DTFT of the ADC has replicas at frequenciesfin i fs/NM. El-Chammas (TI) Time-Interleaved ADCsDec. 201147 / 158 Some notesGain and offset mismatch are static errorsImpact independent of input frequencyBut .. what if gain is a function of frequency?(which it is)And .. what if the gain transfer function varies?(which it will)You have bandwidth mismatch ..M. El-Chammas (TI) Time-Interleaved ADCsDec.

10 201148 / 158 Some notes .. continuedTiming skew is not a static errorSampling Error Due to Timing SkewSkewErrorErrorx(t)Ideal Sampling PointActual Sampling PointSkewIdeal Sampling PointActual Sampling Pointx(t)tt18 Fast signals suffer moresampling error due to timing skew than slow signals Fast signals suffer more sampling error due to timing skew than slow signalsM. El-Chammas (TI) Time-Interleaved ADCsDec. 201149 / 158 Why is timing skew such a problem? adcs aregenerallyuniform sampling systemsWhat if two consecutive samples aren t at timesnTsand (n+ 1)Ts?IIf the deviation is random, you have jitterIIf the deviation is deterministically time -varying because you areinterleaving, you have timing skewITiming skew becomes jitter asN M. El-Chammas (TI) Time-Interleaved ADCsDec. 201150 / 158 How much of a problem is timing skew?InterleaveN B-bit sub-ADCsInput signal is sinusoid with frequencyfin = (NN 1) (122B) (23(2 fin)2)(10)[Jenq 1988]M.